The functions on Rd−1 × (0,∞) (d ≥ 3) that are annihilated by the Laplace– Beltrami operator corresponding to the line-element dl2 = x2 d(dx21 +. . .+dx2 d) are called modified harmonic. In this note, we prove a conjecture of Heinz Leutwiler concerning the space of homogeneous modified harmonic polynomials of a fixed degree.
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Eleutherius Symeonidis (2024) studied this question.
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